the bake star bakery used 2 1/4 cups of raisins to make 4 servings of trail mix. How many cups of raisins are in each serving?

Final answer:

The expression 5 Square root of 1215^x can be simplified to 5^(1+x/2) × 3^(5x/2) by factoring 1215 and applying exponent rules.

Explanation:

To find what is equivalent to 5 Square root of 1215^x, we need to simplify the radical expression and apply exponent rules. The number 1215 can be factored into 3^5 × 5. Therefore, the square root of 1215 is the square root of each factor raised to the power of x. We know that the square root of a number can be expressed as the number raised to the power of 1/2. So 1215 raised to the power x can be expressed as (3^5 × 5)^x, and taking the square root gives us (3^5 × 5)^(x/2).

Applying exponent rules, like multiplying powers when the same base is raised to two different exponents (as per Eq. A.8 and what we know from Integer Powers), we can simplify the expression further. Our expression of 5 times the square root of 1215 raised to the power x becomes 5 × 3^(5x/2) × 5^(x/2).

We can then combine the coefficients (5 × 5^(x/2)) which simplifies to 5^(1+x/2). Our final expression of the original problem then becomes 5^(1+x/2) × 3^(5x/2), which is the simplified version of the original expression.

The value of the equation A = 837.2 / 1.3 is A = 644

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be p

The value of p = 837.2

Let the second number be q

The value of q = 1.3

Now , the equation A = p/q

Substituting the values in the equation , we get

A = 837.2 / 1.3

On simplifying the equation , we get

A = 644

Therefore , the value of A is 644

Hence , the equation is A = 644

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Answer:

Step-by-step explanation:

General Solution

Left hand side

tan(30) + 1 / tan(30

tan^2(30) + 1

============

tan 30

but tan^2(30) + 1 = sec^2(30)

sec^2(theta) / tan(30) Let theta = 30o. This will work for any angle between 0 and 90

[tex]\dfrac{sec^2(theta)}{tan(theta)} = \dfrac{sec^2(theta)}{\dfrac{sin(theta)}{cos(theta)}} = \dfrac{1}{\dfrac{cos^2(theta)*sin(theta)}{cos(theta)}}[/tex]

Cancel out cos(theta) and one of cos^2(theta)

leaving your with

[tex]\dfrac{1}{sin(theta)*cos(theta)}[/tex]

which is exactly what the right hand side is.

This is the way this problem should be done. If you want to show what happens with 30o then

Thirty degree angle

tan(30) = 0.5774

Left hand side

0.5774 + 1/(0.5774) = 2.3093

Right hand side

1/(sin(30)*cos(30))

1/(0.5 * 0.8660)

1/(0.4330

2.3094

Which is about as close as you will get when you round.

Answer:

y = 9x - 5

Step-by-step explanation:

Any line parallel to the given line y = 9x must also have the slope 9.

Substitute the known values (m = 9, h = 0, k = -5) into the point-slope equation of a straight line:

y - (-5) = 9(x - 0)

Then y + 5 = 9x, or

         y = 9x - 5

The subject of this question is Mathematics.

As a tutor, I would need more information about the specific question or problem you are working on to provide a detailed answer. Mathematics encompasses a wide range of topics including algebra, geometry, statistics, and calculus, among others. If you can provide more details about the specific topic or concept you are struggling with, I can provide a step-by-step explanation to help you understand.

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Answer:

= -7

Step-by-step explanation:

6 ⁹ ×6^x = 6²

From the laws of indices;

aⁿ × aⁿ = a^2n

Therefore;

6 ⁹ ×6^x = 6^(9+x)

6^(9+x) = 6²,

Since the bases are the same then the exponents are equal;

9+x = 2

x = -7

Answer:

x=-7

Step-by-step explanation:

[tex]6^9 \cdot 6^x = 6^2[/tex]

Apply exponential property to solve for x

[tex]a^m \cdot a^n = a^{m+n}[/tex]

[tex]6^9 \cdot 6^x = 6^{9+x}[/tex]

So the given equation becomes

[tex]6^{9+x}= 6^2[/tex]

Both sides of the equation has same base 6

So we equate the exponent and solve for x

[tex]9+x= 2[/tex]

Subtract 9 from both sides

[tex]x=-7[/tex]

200,000/52 weeks in a year =$3846.153846 each week

Her weekly paycheck is 3835.82

As we know that there are 52.14 weeks in a year

So weekly paycheck will be 200,000 / 52.14 = 3835.82

Since she gets weekly check so her weekly paycheck is 3835.82

Answer:

You must be no older than 13 to play a game.

Step-by-step explanation:

≤ this sign means equal to or less than in this case it is 13

The situation that should be modeled by the inequality g ≤ 13 is option b.

Inequality function g ≤ 13

We know that ≤ this sign represent that it is equal or lower than So here it should be no older than 13 for playing the game.

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Answer:

128 fluid ounces

Step-by-step explanation:

There are 8 fluid ounces in 1 cup.

There's 1 cup in 8 fluid ounces

16 cups x 8 = 128 fluid ounces

Answer:

see explanation

Step-by-step explanation:

(a)

Consider the factors of the coefficient of the y² term ( - 12) which sum to give the coefficient of the xy- term (- 4)

The factors are - 6 and + 2

since - 6 × 2 = - 12 and - 6 + 2 = - 4, hence

x² - 4xy - 12y² = (x - 6y)(x + 2y)

----------------------------------------------------

(b)

Consider the factors of + 12 which sum to give + 8

The factors are + 2 and + 6, hence

x² + 8x + 12 = (x + 2)(x + 6)

Answer:

0.4

Step-by-step explanation:

0.4 as a percentage is 40%

25% is obviously 25%

10 is also obviously 10%

Answer:

diameter ≈ 11 feet

Step-by-step explanation:

The area (A) of a circle is calculated using the formula

A = πr² ← r is the radius

To find r divide both sides of the equation by π

r² = [tex]\frac{A}{\pi }[/tex] = [tex]\frac{95.03}{\pi }[/tex]

Take the square root of both sides

r = [tex]\sqrt{\frac{95.03}{\pi } }[/tex] ≈ 5.5 feet

Diameter = 2r = 2 × 5.5 = 11 feet

A circle is a curve sketched out by a point moving in a plane. The diameter of the circle whose area is 950.3 square feet is 11 feet.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

As it is given that the area of the circle is 95.03 square feet. Therefore, if we apply the area of the circle, we will get,

[tex]\text{Area of the circle} = \pi r^2[/tex]

where r is the radius of the circle,

[tex]\rm 95.03 = \pi r^2\\\\r = \sqrt{\dfrac{95.03}{\pi}}\\\\r = 5.4999 \approx \rm 5.5\ feet[/tex]

The radius of the circle is half the diameter of the circle, therefore, the diameter of the circle,

[tex]\rm Radius = \dfrac{Diameter}{2}\\\\5.5 \times 2 = Diameter\\\\Diameter = 11\ feet[/tex]

Thus, the diameter of the circle whose area is 950.3 square feet is 11 feet.

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Answer:

21 inches

Step-by-step explanation:

May had just over 6 inches of rain, June had just about 9 inches of rain, and July had just under 6 inches of rain. Together, these months had 9 + 6 + 6 = 21 inches of rain.

Answer:

The discount is $109.50

The sale price is $255.50

Step-by-step explanation:

step 1

Find the discount

we know that

The discount is equal to the original price multiplied by the percentage rate of discount

we have

The original price is $365

The percentage of discount is equal to 30%

30%=30/100=0.30

so

the discount is equal to

0.30*($365)=$109.50

step 2

Find the sale price

The sale price is equal to the original price minus the discount

so

$365-$109.50=$255.50

Answer:

(a - 7)(3 - x)

Step-by-step explanation:

Given

3(a - 7) - x(a - 7) ← factor out (a - 7) from both terms

= (a - 7)(3 - x)

Answer:

Option B.

Step-by-step explanation:

Let

s-----> the number of songs that Eva downloaded

we know that

The linear equation that represent the situation is

[tex]1.29s=11.61[/tex]

Solve for s

Divide by 1.29 both sides

[tex]s=11.61/1.29[/tex]

[tex]s=9\ songs[/tex]

therefore

Ari's work is correct

Answer:

answer b

Step-by-step explanation:

i took test

Answer:

[tex]\large\boxed{RT=\sqrt{165}}[/tex]

Step-by-step explanation:

PT = NT. Therefore we have the equation:

[tex]4x-17=x+10[/tex]       add 17 to both sides

[tex]4x=x+27[/tex]          subtract 4x from both sides

[tex]3x=27[/tex]         divide both sides by 3

[tex]x=9[/tex]

Therefore

[tex]NT=4(9)-17=36-17=19[/tex]

Use the Pythagorean theorem:

[tex]RT^2+RN^2=NT^2[/tex]

Substitute RN = 14 and NT = 19:

[tex]RT^2+14^2=19^2[/tex]

[tex]RT^2+196=361[/tex]           subtract 196 from both sides

[tex]RT^2=165\to RT=\sqrt{165}[/tex]

Answer:

B

Step-by-step explanation:

Given

V = [tex]\frac{Bh}{3}[/tex]

Substitute the given values for B and h into the formula

V = [tex]\frac{15(28)}{3}[/tex] = [tex]\frac{420}{3}[/tex] = 140 in³

Answer:

see explanation

Step-by-step explanation:

the fraction is boys over total in class, that is

fraction of boys = [tex]\frac{8}{24}[/tex] ( divide top/bottom by 8 )

fraction of boys = [tex]\frac{1}{3}[/tex] ← in simplest form

(b)

The number of girls in class = 24 - 8 = 16

fraction of girls = [tex]\frac{16}{24}[/tex] ( divide top/bottom by 8 )

fraction of girls = [tex]\frac{2}{3}[/tex] ← in simplest form

The number of boys is 1/3

The number of girls is 2/3

Total no of students = 24

No of boys in the class is 8

So in fraction form

Boys = 8 out of 24 which is 8/24 or simply 1/3

Now

For girls

no of girls will be Total students - boys students

Number of girls students = 24 - 8 = 16

In fraction form we can write 16/24 or simply 2/3

Answer:

a = 9.632  and b is 10

9.632*10^10 in^3  scientific form

96,320,000,000   in^3  standard form

Step-by-step explanation:

To find volume of a rectangular prism

V = l*w*h

   = 1.4 * 10^4   ( 4.3 * 10^3)   (1.6* 10^3)

When multiply powers of 10, we multiply the numbers out front

1.4*4.3*1.6 =9.632

Then we add the powers of 10

10^(4+3+3)

10^10

The volume is 9.632*10^10 in^3

a = 9.632  and b is 10

In standard form we move the decimal 10 places to the right.  If there are not enough numbers we add zeros

9.632*10^10 in^3

96,320,000,000   in^3

Answer:

x would equal -4

Step-by-step explanation:

Answer:

The answer is D.

Step-by-step explanation:

Count how many l's there are, how many h's there are, and how many w's there are.

Answer:

[tex]\large\boxed{B.\ S.A.=2lw+2lh+2wh}[/tex]

Step-by-step explanation:

It's the net of a rectangular prism.

The formula of a surfave area of a rectangular prism:

[tex]S.A.=2lw+2lh+2wh[/tex]

We have two rectangles l × w, two rectangles l × h and two rectangles w × h.

Answer:

[tex]\frac{19}{9}[/tex]

Step-by-step explanation:

To change the mixed number to an improper fraction.

Multiply the whole number by the denominator of the fraction and add the numerator. The denominator remains unchanged, that is

2 [tex]\frac{1}{9}[/tex]

=[tex]\frac{2(9)+1}{9}[/tex] = [tex]\frac{19}{9}[/tex]

Answer:

C

Step-by-step explanation:

The sum to infinity of a geometric series is

[tex]\frac{a_{1} }{1-r}[/tex] ( - 1 < r < 1 ) ← substitute values

S( ∞ ) = [tex]\frac{5}{1-\frac{1}{3} }[/tex] = [tex]\frac{5}{\frac{2}{3} }[/tex] = [tex]\frac{15}{2}[/tex]

The sum of the infinite geometric series is [tex]\frac{15}{2}[/tex]

The sum of all the terms of a geometric sequence is called infinite geometric series.

If a, ar, a[tex]r^{2}[/tex], ...., a[tex]r^{n-1}[/tex], .... is a geometric series, then  a+ar+a[tex]r^{2}[/tex]+ ....+a[tex]r^{n-1}[/tex]+.... is the corresponding infinite geometric series.

where a is the 1st term & r is the common ratio between consecutive terms of the series.

Sum of infinite geometric series = [tex]\frac{a}{1-r}[/tex] ; |r|<1

Given, 1st term ([tex]a_{1}[/tex]) of the infinite geometric series = 5

Common ratio (r) = 1/3

∴ Sum of infinite geometric series = [tex]\frac{a_{1} }{1-r}[/tex]

                                                         = [tex]\frac{5}{1-\frac{1}{3} }[/tex]

                                                         = [tex]\frac{5}{\frac{2}{3} }[/tex]

                                                         = [tex]\frac{15}{2}[/tex]

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Answer:

c.200

Step-by-step explanation:

The Answer Is J.14.50

Answer: $14.50

Step-by-step explanation:

Multiply $5.95 by 2.

Multiply $0.65 by 4.

Add both of the answers to the multiplying problems

Your final answer... I hope I was able to help!

Answer:

2)    (1,1.5)

4) Not enough information

Step-by-step explanation:

2) If you look along at the intersection point of the two lines it's (1,1.5).

4) Since only one equation is graphed, we can't tell anything.